Timeline for An algebraic group $G$ over $L^+$ such that $G_{\mathbb{R}}$ is compact for almost all embeddings
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| 1 hour ago | history | edited | LSpice | CC BY-SA 4.0 |
Typo
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| 1 hour ago | comment | added | paul garrett | @PolvanHoften, of course it would be more stable, here, if you wrote your excellent "comments" as "an answer". :) | |
| S 1 hour ago | history | suggested | J. W. Tanner | CC BY-SA 4.0 |
Corrected spelling in ititle
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| 5 hours ago | comment | added | ALi1373 | Thank you very much. | |
| 7 hours ago | review | Suggested edits | |||
| S 1 hour ago | |||||
| 8 hours ago | comment | added | Pol van Hoften | ... We need to show that there is a class in $H^1(L^+,G)$ whose image in $H^1(L^+_{v},G)$ for infinite places $v$ of $L^+$ corresponds to the compact inner form of $G_{\mathbb{R}}$ for all but one $v$. This can always be done using the short exact sequence abpve, by choosing nontrivial classes at some auxiliary finite places. In fact, a single finite place should be enough since I think that $\pi_1(G)=\mathbb{Z}/2\mathbb{Z}$ with trivial Galois action. | |
| 8 hours ago | comment | added | Pol van Hoften | Yes such a group should exist. For example it can be constructed as an inner form of the split adjoint group $G$ of type $E_7$ using the short exact sequence of pointed sets $H^1(L^+, G) \to \bigoplus_{v} H^1(L^+_{v},G) \to \pi_1(G)_{\Gamma_{L^+}}$. Here $\pi_1(G)$ is Borovoi's algebraic fundamental group and $\Gamma_{L^+}$ is the absolute Galois group of $L^+$.... | |
| 12 hours ago | history | edited | Bugs Bunny | CC BY-SA 4.0 |
Two possible typos
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| 12 hours ago | history | asked | ALi1373 | CC BY-SA 4.0 |